International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 473-482
doi:10.1155/S0161171287000553

A new class of composition operators

S. Pattanayak, C. K. Mohapatra, and A. K. Mishra

School of Mathematical Sciences, Sambalpur University, Jyoti Vihar 768019, India

Received 30 May 1984; Revised 14 June 1985

Copyright © 1987 S. Pattanayak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new class of composition operators Pϕ:H2(T)→H2(T), with ϕ:T→D¯ is introduced. Sufficient conditions on ϕ for Pϕ to be bounded and Hilbert-Schmidt are obtained. Properties of Pϕ with ϕ(eit)=aeit+be−it for different values of the parameters a and b have been investigated. This paper concludes with a discussion on the compactness of Pϕ.